Question

What operator can fill in the blank?
6 - 1/4 x 28 - 2 1/4 ??? 3/4 + 4 x 2 - 11

Answer 1

To determine what operator can fill in the blank, we need to evaluate the expression:

\[ 6 - \frac{1}{4} \times 28 - 2 \frac{1}{4} \, ? \, \frac{3}{4} + 4 \times 2 - 11 \]

Let's break it down step by step.

1. **Calculate \( 6 - \frac{1}{4} \times 28 \):**
\[
\frac{1}{4} \times 28 = 7
\]
Therefore,
\[
6 - 7 = -1
\]

2. **Convert \( 2 \frac{1}{4} \) to an improper fraction:**
\[
2 \frac{1}{4} = \frac{9}{4}
\]

3. **Now our expression looks like:**
\[
-1 - \frac{9}{4} \, ? \, \frac{3}{4} + 4 \times 2 - 11
\]

4. **Calculate \( 4 \times 2 \):**
\[
4 \times 2 = 8
\]

5. **Updating our expression:**
\[
-1 - \frac{9}{4} \, ? \, \frac{3}{4} + 8 - 11
\]

6. **Now simplify \( 8 - 11 \):**
\[
8 - 11 = -3
\]

7. **Updating our expression again:**
\[
-1 - \frac{9}{4} \, ? \, \frac{3}{4} - 3
\]

8. **Convert \(-1\) into a fraction with \(4\) as the denominator:**
\[
-1 = -\frac{4}{4}
\]
Thus,
\[
-\frac{4}{4} - \frac{9}{4} - 3 = -\frac{13}{4} - 3 = -\frac{13}{4} - \frac{12}{4} = -\frac{25}{4}
\]

So now we have:
\[
-\frac{25}{4} \, ? \, \frac{3}{4}
\]
The question now is to find an operator to compare \(-\frac{25}{4}\) and \(\frac{3}{4}\).

Now we will check different comparisons on whether we need \(> (<, =)\):

Since \(-\frac{25}{4} = -6.25\) and \(\frac{3}{4} = 0.75\):
- It is clear that \(-6.25 < 0.75\).

Thus, we can use the operator \(<\) to fill in the blank:

\[
6 - \frac{1}{4} \times 28 - 2 \frac{1}{4} < \frac{3}{4} + 4 \times 2 - 11
\]

The answer is \( < \).